Setting exact scale/dimension on multiple objects as a whole
For the first part of your questions, it is possible to set transforms on multiple objects: Select the objects, and hold down the Alt key when clicking on a channel in the transforms panel. Enter your desired value. As soon as you hit Enter this value gets applied on all selected objects. You'll need to repeat this channel by channel. This by the way works in many areas of Blender already, not only on transform channels.

To set the origin of all objects to one specific location you can set the Cursor to the desired location first, and then use Ctrl+Shift+Alt+C, which gives you this menu here:



Setting the dimensions as a whole: I assume you want to define the size of the 'bounding box' of a bunch of selected objects, so the selection kind of fits into a box which dimensions you want to define numerically. This is afaik only possible if you really join the meshes together. The dirty hack would be to drop in a cube, set its dimensions to your desired target values, set the 3D cursor as the scaling center, align the bottom of this cube to the bottom of your objects to scale, snap the cursor to the center of one of the cube's faces, and scale the selection up manually until it fills the volume. Not really fast, but doable.